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Two trains one travelling at 54 kmph and...

Two trains one travelling at 54 kmph and the other at 72 kmph are headed towards one an other along a straight track. When they are `1/2` km apart, both drivers simultaneously see the other train and apply their brakes. If each train is decelerated at the rate of `1 ms^(-2)` , will there be collision ?

Text Solution

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Distance travelled by the first train before coming to rest
`s_(1)=(u^(2))/(2a)=(72xx(5)/(18))^(2)//2xx1=(400)/(2)=200m`
`=(225)/(2)=112.5m`
Distance travelled by the second train before coming to rest
`s_(2)=(72xx(5)/(18))^(2)//2xx1=(400)/(2)=200m`
Total distance travelled by the two trains before coming to rest `=s_(1)+s_(2)=112.5+200=312.5m`
Because the initial distance of separation is 500 m which is greater than 312.5 m, there will be no collision between the trains.
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